Filter with surface acoustic wave resonators

ABSTRACT

A filter with surface acoustic wave resonators using an equivalent electrical bridge structure to obtain a good form relationship, i.e., a relationship between the filter rejection band and its pass band. Bridge arms advantageously include the paralleling of several resonators, thereby not requiring additional electrical elements as in the background art which provides for the use of series-connected resonators. Particular implantation methods for preparing equivalent structures to paralleling several resonators are also disclosed.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The field of the invention is that of surface-acoustic-wave filters withhighly frequency selective performance characteristics, namelyrelatively small bandwidths with high rejection qualities. The term<<surface wave >> is understood here to mean not only Rayleigh waves butalso any type of wave that can interact with interdigitated electrodeson the surface of a crystal or at the interface between a crystal andone or more layers of any material. The waves known as Pseudo SAW orLeaky SAW waves, the waves known as Surface Transverse Waves or SSBW(Surface Skimming Bulk Waves) may thus be considered to be surface wavesand the invention can be applied to this type of wave as well as to anytype of wave that meets the above conditions.

2. Discussion of the Background

In general, to obtain performance characteristics of this kind, filtersare used with resonators conventionally formed by transducers containedin a cavity formed by two periodic arrays as shown in FIG. 1. Morespecifically, these are multipole filters obtained by coupling severalresonators. It is sought indeed to couple the greatest number ofresonators since the number of resonators coupled to each othergenerally determines the shape factor of the filter, namely the ratiobetween the rejection band of the filter and its passband. The increasein the number of resonators makes it possible to approach a shape factorof 1.

At present, there are known ways of making a surface-acoustic-wavefilter configuration with two poles comprising a first pair ofresonators IDT₁ with a center frequency f₁, a second pair of resonatorsIDT₂ with a center frequency f₂, the set of two pairs being mounted inan <<electrical equivalent >> bridge structure as shown in FIG. 2. Thistype of configuration is described in the U.S. Pat. No. 5,508,667.

The value of this structure lies in the fact that the product of thestatic capacitances of the first pair is the same as the product of thestatic capacitances of the second pair. This balancing makes it possibleto ensure rejection by the filter far from its center frequency. Indeed,far from this frequency, the resonators are electrically equivalent totheir static capacitance and the balancing makes it possible to preventany signal from passing through.

To further increase the performance characteristics of the resonatorfilters, it is planned to set up a series cascade of several “electricalequivalent” bridge structures. Most frequently, identical bridges arecascade-connected with one another. The drawback of a structure of thiskind lies in the fact that this cascade, in order to be efficient,requires the addition of a supplementary electrical element (an inductoror a capacitor). Furthermore, the use of several cascade-connected“bridges” is an obstacle as regards the mounting inside the pack of thefilter.

SUMMARY OF THE INVENTION

This is why the invention proposes a filter structure that makes itpossible to do away with the need for the coupling inductance in which asingle equivalent bridge structure may comprise a large number of poles,through a parallel connection of different resonators in each arm of thebridge.

More specifically, an object of the invention is a surface-acoustic-wavefilter with N poles, N being a number greater than or equal to 3 andcomprising a set of resonators, characterized in that:

the resonators are electrically coupled to form a four-arm electricalbridge;

two arms comprising two identical sub-assemblies E₁ and E₃ of N₁resonators each parallel-connected;

two arms comprising two identical sub-assemblies E₂ and E₄ of N₂resonators each parallel-connected;

with N₁+N₂=N;

the product of the total static capacitance of the sub-assembly E₁multiplied by the total static capacitance of the sub-assembly E₃ bringsubstantially equal to the product of the total static capacitance ofthe sub-assembly E₂ multiplied by the total static capacitance of thesub-assembly E₄, so as to balance the electrical bridge.

According to a first variant of the invention, if N is an even number,N₁=N₂=N )/2.

According to a second variant of the invention, if N is an odd number,N₁=(N−1)/2 et N₂=(N+1)/2.

According to the filter configuration proposed in the invention, theparallel connection of the resonators requires connection wires ortracks on the substrate to make the bridges. To overcome this obstacle,a preferred mode of the invention consists not in making the parallelconnection of the resonators physically but rather of the use, in thedifferent arms of the bridge, of surface wave devices behaving likeseveral parallel-connected resonators.

This is why, in at least one of the arms of the electrical bridge, thesurface-acoustic-wave filter may comprise a single surface wave devicehaving an admittance equivalent to the parallel connection of asub-assembly of resonators.

In particular, the filter according to the invention may becharacterized in that at least one arm comprises a structure equivalentto several parallel-connected resonators, said structure comprising twonetworks of interdigitated electrodes constituting the transduction partof the resonator, said networks being connected to two buses withdifferent polarities in comprising m acoustic channels inserted betweenthe two buses, the i^(th) channel possessing a pitch p_(i) of electrodeson a length of electrodes w_(i) and 1≦i≦m.

According to one variant of the invention, the i^(th) acoustic channelmay comprise two reflective arrays on each side of the transductionpart.

According to one variant of the invention, the surface-acoustic-wavefilter may comprise, in at least one of the arms of the electricalbridge, a structure equivalent to at least two parallel-connectedresonators, said structure comprising two interdigitated electrodearrays, said arrays being connected to a first bus and a second bus withdifferent polarities so as to define a transducer having a central axisZ parallel to the electrodes, said arrays comprising a part of theirelectrodes positioned symmetrically with respect to the central axis,the transducer also comprising electrodes positioned symmetrically withrespect to the central axis and connected to buses with differentpolarities so as to excite symmetrical longitudinal modes andantisymmetrical longitudinal modes. The arrays of electrodes may or maynot be inserted between reflector arrays.

According to another variant of the invention, the surface acousticfilter comprises, in at least one of the arms of the electrical bridge,a DART type resonator with transduction cells interposed betweenreflection cells.

Advantageously, the DART type resonator may comprise resonant cavities.

When the number of poles is an even number, the distance between thetransduction center of a transduction cell and the reflection center ofthe reflection cell adjacent to said transduction cell may preferably bein the range of (3±d)λ/8+kλ/2, with λ being the wavelength correspondingto the center frequency of the filter, d being smaller than 1 and kbeing an integer.

BRIEF DESCRIPTION OF THE DRAWINGS

Finally, according to another variant, the surface-acoustic-wave filtercomprises a series connection of several sets of resonators, of which atleast one set of resonators corresponds to those of the invention.

The invention will be understood more clearly and other advantages shallappear from the following description, given as a non-restrictiveexample with reference to the appended drawings, of which:

FIG. 1 gives a schematic view of a resonator with a transducer insertedbetween reflective arrays;

FIG. 2 illustrates configuration of a prior art filter mounted in abridge structure;

FIG. 3 gives a schematic view of a general configuration of asurface-acoustic-wave filter according to the invention;

FIG. 4 illustrates an installation of a prior art two-polesurface-acoustic-wave filter;

FIG. 5a gives a schematic view of an installation of asurface-acoustic-wave filter comprising two parallel-connectedresonators;

FIG. 5b illustrates a first exemplary resonator installation equivalentto two parallel-connected resonators shown in FIG. 5a;

FIG. 6 illustrates a second exemplary installation of a resonatorequivalent to two parallel-connected resonators, using three acousticchannels;

FIG. 7 illustrates a third exemplary installation of a resonatorequivalent to two parallel-connected resonators using two acousticchannels, but offset by a pitch p_(i);

FIG. 8 illustrates a fourth exemplary installation of a resonatorequivalent to two parallel-connected resonators, using the excitation ofsymmetrical modes and antisymmetrical modes longitudinally;

FIG. 9 illustrates the admittance of an exemplary DART type transducerin which the center of a transduction cell is separated from the centerof an adjacent reflection cell by a distance 3λ/8;

FIG. 10 illustrates the progress of the conductance of the same DARTtype transducer in which the center of a transduction cell is separatedfrom the center of an adjacent reflection cell by a distance varyingfrom (3−0,4)λ/8 to (3+0,4)λ/8;

FIG. 11 illustrates the progress of the susceptance of the same DARTtype transducer in which the center of a transduction cell is separatedfrom the center of an adjacent reflection cell by a distance varyingfrom (3−0,4)λ/8 to (3+0,4)λ/8;

FIG. 12 illustrates the transfer function for an exemplary four-polefilter according to the invention, using DARTs;

FIG. 13 illustrates the admittance of an electrical bridge armcomprising a two-mode DART used in an exemplary filter according to theinvention with three poles;

FIG. 14 illustrates the admittance of the second electrical bridge armcomprising a non-weighted DART in an exemplary filter according to theinvention with three poles;

FIG. 15 illustrates the transfer function of the same exemplary filteraccording to the invention with three poles, comprising a one-moderesonator in one arm and a two-mode resonator in the other arm;

FIG. 16 illustrates the conductance values of two resonators used in anexemplary 87 MHz filter according to the invention using resonators ofthe type shown in FIG. 6;

FIG. 17 illustrates the susceptance values of two resonators used in anexemplary 87 MHz filter according to the invention using resonators ofthe type shown in FIG. 6;

FIG. 18 illustrates the installation of the filter whose characteristicsare given in FIGS. 15, 16 and 17;

FIG. 19 illustrates the transfer function of the 87 MHz filter madeaccording to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The general configuration of a surface-acoustic-wave filter according tothe invention is shown schematically in FIG. 3. It comprises a structurein the form of an equivalent bridge formed by four arms, each armcomprising a set of parallel-connected resonators connected to an input(E+, E−) and an output (S+, S−). The center frequencies of theresonators f₁, f₂ . . . f_(N) corresponding to the poles of the filteras well as the “couplings” of the different resonators are chosen toobtain the desired filtering function.

For a clear understanding of the operation, it is necessary to take acloser look at the working of a resonator. In general, it may beconsidered that, near the resonance frequency, the equivalent diagram ofa resonator is given by a static capacitance in parallel with a seriesresonant circuit at the frequency f_(s).

The admittance of the resonator is therefore the following (if weoverlook the resistance Rs) where f is the frequency and ω is thepulsation (ω=2ηf)${Y(f)} = {{{j\quad \omega \quad {Cp}} + \frac{1}{{Rs} + {{jLs}\quad \omega} - \frac{j}{{Cs}\quad \omega}}} \cong {{j\quad \omega \quad {Cp}} - {\frac{j\quad {Cs}\quad \omega}{{{LsCs}\quad \omega^{2}} - 1}\begin{matrix}{{{Y(f)} \cong \quad {{j\quad \omega \quad {Cp}} - \frac{j\quad 2\pi \quad {Csf}}{4\quad \pi^{2}{Ls}\quad {Cs}\quad ( {f^{2} - {fs}^{2}} )}}} = {{j\quad \omega \quad {Cp}} - {j\quad \frac{f}{2\quad \pi \quad {Ls}\quad ( {f^{2} - {fs}^{2}} )}}}} \\{= \quad {{j\quad \omega \quad {Cp}} - {j\quad \frac{2\quad \pi \quad {Csfs}^{2}f}{( {f^{2} - {fs}^{2}} )}}}}\end{matrix}}}}$

It is therefore possible to express the admittance of a resonator in theform of the sum of a capacitive term related to the parallel capacitanceCp and a resonant term proportional to the coefficient a:${{Y(f)} \cong {{j\quad \omega \quad {Cp}} - {j\quad \frac{af}{( {f^{2} - {fs}^{2}} )}a}}} = {\frac{1}{2\quad \pi \quad {Ls}} = {2\pi \quad {Csfs}^{2}}}$

The coefficient a (proportional to the series capacitance of theresonator) determines the “coupling” of the resonance mode considered atthe electrical access. It shall hereinafter be called the coupling ofthe mode.

An ideal resonator will therefore be characterized by the resonant partof its admittance which has the form:${{- a} \cdot j}\quad \frac{f}{f^{2} - f_{s}^{2}}$

and which therefore has a pole at the frequency ±f_(s). In practice,owing to the non-zero losses in the resonators which are approximatelyequivalent to a series resistance on the resonant part, the resonantterm of the admittance is written as follows:$\frac{C_{s}\quad \omega}{{R_{s}C_{S}\omega}\quad + {{jL}_{s}{C_{s}\lbrack {\omega^{2} - \omega_{s}^{2}} \rbrack}}}$

The pole at the frequency f=f_(s) (where ω=ω_(s)) is no longer a truepole since it is dampened. In other words, the losses convert the poleat the frequency f=f_(s) into a pole with a complex real part close tof_(s) and an imaginary part that is all the greater as the losses aregreat. A resonator is therefore characterized by an admittancecomprising a resonance which may or may not be dampened and thereforehas a pole on a frequency close to the real axis.

In this configuration, each of the arms comprises two parallel-connectedresonators.

We shall now describe the invention in detail in the case of a four-polesurface-acoustic-wave filter.

According to the prior art, when it is sought to lay out a four-armelectrical bridge structure, each arm comprising a resonator, it ispossible to design a symmetrical structure needed for the balancing ofthe bridge, and hence for the rejection qualities of the filter, with aninstallation of the type shown schematically in FIG. 4.

This installation has the advantage of being symmetrical to the back ofthe pack, even with regard to the parasitic capacitances. The surfaceareas of the reflector arrays R_(i) are the same for the two ports,namely the + and − ports. Furthermore, the ground is not connected tothe filters since the arrays are all connected to one of theinput/output ports, thus making it possible to overcome any imbalancesof the electrical source and load circuits more efficiently.

However, the symmetry that can be obtained with the installationdescribed here above is more difficult to obtain when the number ofpoles is increased.

This is why, the invention proposes to replace the parallel connectionof several resonators by making resonators that are equivalent to thisparallel connection and that use only two connection buses and no longerfour in the case of a parallel connection of two resonators (two inputs,two outputs).

In particular, it is possible to make a resonator equivalent to twoparallel-connected resonators by separating the acoustic aperture intotwo channels and interconnecting the electrodes of two channels so as tohave, on each of the two channels, the sequence corresponding to one ofthe two transducers. As an example, FIG. 5a shows a possibleinstallation for an assembly of two parallel-connected resonators.

FIG. 5b illustrates an equivalent installation in which the first upperacoustic channel is made by means of electrodes that are interdigitatedat the pitch p₁, the second lower acoustic channel being made by meansof electrodes that are interdigitated at the pitch p₂. The two channelsare electrically connected by metallizations m₁ shown symbolically inthe figures.

The pitch values p₁ and p₂ govern the resonance frequencies of theresonator equivalent to the two parallel-connected resonators. Thedimensions w₁ and w₂ condition the coupling of these resonators so as toobtain the characteristics of the filter to be manufactured. FIGS. 5aand 5 b show only the transducer part of the resonators. According tothe prior art, the resonators generally comprise two reflector arrays oneither side of a transducer. The reflector arrays are omitted in thefigure but may be added on each of the channels. The arrays of each ofthe channels may be connected or not connected together. Preferably, forthe reflector arrays of the different channels, the periods chosen areproportional to the periods of the transducers. In other words, if p_(i)and p_(j) are the periods of the two transducers and P_(Ri) and PrR_(j)are the periods of the arrays, the following will be chosen:$\frac{P_{i}}{P_{j}} = \frac{{PR}_{i}}{{PR}_{j}}$

Similarly, if Δ and Δ′ are the distances between the reflector arraysand the transducers, the following will be chosen preferably:$\frac{\Delta \quad i}{\Delta j} = {\frac{Pi}{Pj}.}$

In this way, the two channels are homothetical with each other.

Finally, for the filters having more than four poles, it becomesnecessary to place more than two resonators in parallel. It is evenpossible, in the same way as here above, to use several acousticchannels and connect the metallizations of the different channelstogether to set up the parallel connection.

However, in this type of configuration, when the two acoustic channelswith sizes w₁ and w₂ are too close to each other, phenomena of parasiticacoustic crosstalk appear between the channels.

This is why, to eliminate this type of crosstalk, the invention alsoproposes another structure shown in FIG. 6. For this purpose, thecentral channel, which generates an excitation that is symmetrical withthe horizontal axis and is therefore coupled only to waves havingtransversely symmetrical forms, is inserted between two upper and lowerchannels corresponding on the whole to one of the acoustic channelsshown in FIG. 5b. The upper and lower acoustic channels have the samecharacteristics of electrode dimension w₁=W₃ and electrode pitch p₁=P₃.These two channels generate an antisymmetrical excitation with respectto the horizontal axis since the facing electrodes for the two channelsare connected to opposite potentials. These two channels are thereforecoupled only to waves having transversely antisymmetrical forms andthere can therefore be no crosstalk between the central channel and theexternal channels. In other words, owing to the connection of theelectrodes facing the end channels to the opposite bus, the crosstalkbetween the central channel and the top channel gets added up in phaseopposition and therefore gets cancelled out with the crosstalk betweenthe central channel and the lower channel. To obtain compensation forthe coupling phenomena, the electrodes connected to the bus E+ areplaced so as to be facing the electrodes connected to the bus E− on theend channels.

The two resonance frequencies sought in order to reconstitute twoparallel-connected resonators may also be obtained by means of thedifference in speed between the symmetrical and antisymmetricaltransversal modes.

In this case, it is also possible to make a structure in which the pitchvalues p₁ and p₂ are equal. In this particular case, it even becomespossible to make a structure with two acoustic channels as shown in FIG.7. By offsetting the electrodes of the two channels by a distance of p₁from each other, it becomes possible to obtain a compensation, in thesame way as explained here above, in the parasitic coupling phenomenasince it becomes possible to place the electrodes connected to the busE+ so that they face electrodes connected to the bus E−. In thisconfiguration, the central channel becomes aligned with one of the endchannels.

According to another variant of the invention, it is possible to make astructure equivalent to two parallel-connected resonators byparameterizing the number of longitudinal modes created in theresonator.

Indeed, in general, a resonator is a transducer placed between tworeflector arrays. Depending on the period of the array and that of thetransducer and depending on the distance between the arrays and thetransducer, we are in the presence of several longitudinal modes. Thecoupling of a mode depends on the integral of overlapping of theweighting of the transducer on the amplitude of the mode in the cavity.In general, we are in the presence of symmetrical and antisymmetricalmodes. It is possible to weight the transducer so as to obtain thedesired couplings with the symmetrical and antisymmetrical modes.

FIG. 8 shows an exemplary resonator in which it is possible to exciteboth the symmetrical longitudinal modes and the antisymmetricallongitudinal modes.

P_(r) represents the pitch of the constituent elements of the arrays 1and 2. P_(t) represents the pitch of the electrodes of the transducer. Δrepresents the spacing between the transducer and an array. Thetransducer has a dissymmetry with respect to the axis Z centered on thetransducer.

Depending on the periods P_(r) and P_(t), the distance Δ and the numberof periods of the transducer, the resonance cavity will have severalresonance frequencies corresponding to different longitudinaldistributions of energy in the cavity. By appropriately choosing theexcitation, namely the sequence of electrodes of the transducer, it ispossible to excite the symmetrical longitudinal modes and theantisymmetrical longitudinal modes. The weighting of the transducer maybe subdivided into two parts. The symmetrical part (with reference tothe z axis) of the weighting will excite the symmetrical longitudinalmodes while the antisymmetrical part (with reference to the z axis) willexcite the antisymmetrical longitudinal modes. The integral ofoverlapping of the symmetrical (or antisymmetrical) part of theweighting on the amplitude of the symmetrical (antisymmetrical) modeswill be related to the coupling of the symmetrical (antisymmetrical)modes.

The transducer shown in FIG. 8 is neither entirely symmetrical norentirely antisymmetrical and enables the excitation of both symmetricalmodes and antisymmetrical modes so as to reconstitute the intermodecoupling and thus the equivalence with two parallel-connectedresonators.

According to another variant of the invention, the surface-acoustic-wavefilter comprises DART (Distributed Phase Unidirectional Transducer) typetransducers also known in the literature as SPUDT (Single PhaseUnidirectional Transducers).

This type of transducer, which is described in the published patentapplication Ser. No. 2,702 899, is obtained by the interposing, in atransducer, of the cells known as transduction cells and the cells knownas reflection cells and by positioning the cells with respect to oneanother so that the waves sent are reset in phase with the reflectedwaves in the useful direction and are placed in phase opposition in theother direction. For the usual substrates, the distance between thetransduction center and the reflection center must be 3λ/8 so that thephases are correct. More generally, a DART may be considered to be atransducer in which electrodes are distributed. These electrodes aredesigned so that, within the transducer, there is a transductionfunction and a reflection function and so that the transducer has apreferred direction. It was shown in the patent application publishedunder Ser. No. 2,702,899 that it was advantageous to make resonantcavities within the DART, a resonant cavity being made by changing thesign of the reflection function.

It is known that, in the case of a non-weighted DART, namely onecomprising functions of reflection and transduction that are constantand long enough for its overall reflection coefficient to be close to 1,there are two modes existing at the starting and ending frequencies ofthe rejection band of the reflectors. Should the phase differencebetween reflection and transduction correspond to a resetting in phaseof the waves sent and reflected in the useful direction, namely ingeneral should the distance between the transduction center and thereflection center be 3λ/8, the two modes are excited identically and theconductance of the transducer is symmetrical in frequency. By way of anexample, FIG. 9 shows the admittance of a DART transducer with a length200 λ at 109.3 MHz. The thickness of the metallization chosen is 0.7 μmand one reflector with a width of 3λ/8 is used per wavelength. Thetransducer is “ideal”, namely the distance between the transductioncenter and the reflection center is 3λ/8.

FIGS. 10 and 11 show the changes undergone by the conductance andsusceptance values when the distance between the transduction center andthe reflection center varies from 3λ/8−0.05λ to 3λ/8+0.05λ. It can beseen that we are still in the presence of the same two modes but thattheir relative importance varies according to the distance. Furthermore,when the sign of the shift is changed, the same conductance is obtainedfor the modes, except for a symmetry. In the case of a four-pole filter,it is generally useful, in an arm of the electrical bridge, to use modessuch that their coupling is in a ratio of about 2. For example, thefilter according to the invention may comprise, in one of its arms, aDART using a shift of −0.025 λ and, in the other arm, a DART using ashift of +0.025 λ. So as to have four distinct resonance frequencies,the transducer using a −0.025 λ shift has been given a downwardfrequency shift of about 250 kHz. FIG. 12 shows the transfer functionobtained for the electrically tuned filter.

According to another example using DARTs, a three-pole filter may beobtained by using a one-mode resonator in one of the arms and a two-moderesonator in the other arm. The two-mode resonator used in the exampleis a non-weighted DART with a transduction/reflection distance of 3λ/8.The DART has a length of 400 wavelengths. The thickness of themetallization chosen is 0.35 μm and a reflector with a width of 3λ/8 isused per wavelength. The center frequency is 109.8 MHz. FIG. 13 showsthe admittance of the DART with its two modes at the input and output ofthe rejection band. For the other arm of the electrical bridge, it hasbeen chosen to use a DART that has the same length (and hence the samestatic capacitance) and resonates at the center frequency. FIG. 14 showsthe admittance of the non-weighted DART included in the other arm of theelectrical bridge. This has been obtained by inserting a change in signof the reflection function at the center of the transducer. There isthen a single resonance mode.

The transfer function obtained for the three-pole filter is given inFIG. 15.

Exemplary quartz filter at 87 MHz

This is a filter with a passband of about 300 kHz in a very small pack(7 mm×5 mm) with a number of poles N equal to 4.

To achieve this low space requirement of the pack, the resonators useddo not have reflector arrays and are therefore reduced to simpletransducers with two electrodes per wavelength The installation is ofthe type shown in FIG. 18. The lengths of the transducers are 264periods (i.e. a length of 4.75 mm approximately). It we overlook thelosses, the admittance values of the arms are given roughly by:${{Ys}(f)} = {{j( {\frac{a_{1}f}{f^{2} - f_{1}^{2}} + \frac{a_{3}f}{f^{2} - f_{3}^{2}}} )} + {j\quad {Cw}}}$${{Ya}(f)} = {{j( {\frac{a_{2}f}{f^{2} - f_{1}^{2}} + \frac{a_{4}f}{f^{2} - f_{4}^{2}}} )} + {j\quad {Cw}}}$

by choosing:

f₂−f₁=250 kHz

f₃−f₂˜60 kHz and a₂=a₁, a₃=a₄=a₁/2

f₁−f₄˜60 kHz

The characteristics of conductance values and susceptance valuesobtained, as a function of the frequency, are illustrated respectivelyin FIGS. 16 and 17.

To obtain the admittance values desired for the resonators, it is chosento have an aperture and a metallization thickness that provide for adifference of 310 kHz between the resonance frequencies of the firstsymmetrical transversal mode and the first antisymmetrical transversalmode, giving a metallization thickness of 0.8 μm and a transduceraperture of about 300 μm.

The structure of FIG. 7 has been chosen for the resonators.

Thus, for the two resonators, we have the following characteristics:

1st resonator (equivalent to two parallel-connected resonators):

w′₁=210 μm

w′₂=90 μm

2nd resonator (equivalent to two parallel-connected resonators):

w′₁=232,5 μm

w′₂=67,5 μm

The periods of these two resonators are determined so as to accuratelylink the frequencies to each other. That is to say, they areapproximately:

for the first resonator, a period of 17.95 μm

for the second resonator, a period of 17.94 μm

FIG. 18 shows the installation representing the electrical bridge madewith the first resonator in two arms and the second resonator in theother two arms.

For reasons of space requirement, the two inputs E+ areparallel-connected by a wire and not a track.

The filter is designed to work with an impedance value of 4,000Ω with aparallel-connected inductor. Its transfer function is illustrated inFIG. 19.

What is claimed is:
 1. Surface-acoustic-wave filter with N poles, Nbeing a number greater than or equal to 3 and comprising a set ofresonators, characterized in that: the resonators are electricallycoupled to form a four-arm electrical bridge; two arms comprising, twoidentical sub-assemblies E₁ and E₃ of N₁ parallel-connected resonators;two arms comprising two identical sub-assemblies E₂ and E₄ of N₂parallel-connected resonators; with N₁+N₂=N; the product of the totalstatic capacitance of the sub-assembly E₁ multiplied by the total staticcapacitance of the sub-assembly E₃ bring substantially equal to theproduct of the total static capacitance of the sub-assembly E₂multiplied by the total static capacitance of the sub-assembly E₄, so asto balance the electrical bridge.
 2. Surface-acoustic-wave filteraccording to claim 1, characterized in that N is an even number andN₁=N₂=N/2.
 3. Surface-acoustic-wave filter according to claim 1,characterized in that N is an odd number and N₁=(N−1)/2 et N₂=(N+1)/2.4. Surface-acoustic-wave filter according to claim 1, characterized inthat at least one arm comprises a single surface wave device having anadmittance equivalent to the parallel connection of a sub-assembly ofresonators.
 5. Surface-acoustic-wave filter according to claim 1,characterized in that at least one arm comprises a structure equivalentto several parallel-connected resonators, said structure comprising twonetworks of interdigitated electrodes constituting the transduction partof the resonators, said networks being connected to two buses withdifferent polarities in comprising m acoustic channels inserted betweenthe two buses, the i^(th) channel possessing a pitch p_(i) of electrodeson a length of electrodes w_(i) and 1≦i≦m.
 6. Surface-acoustic-wavefilter according to claim 5, characterized in that the i^(th) acousticchannel comprises two reflective arrays on each side of the transductionpart.
 7. Surface-acoustic-wave filter according to claim 5,characterized in that the two consecutive acoustic channels areconnected to each other by metallizations m_(i), connecting theelectrodes separated by a pitch p_(i) to the electrodes separated by apitch p_(i+1).
 8. Surface-acoustic-wave filter according to claim 5,characterized in at least one arm comprises a structure equivalent totwo parallel-connected resonators and said structure comprises an upperacoustic channel and a lower acoustic channel with an electrode pitch p₁and an electrode length w₁, a central acoustic channel with an electrodepitch p₂ and an electrode length w₂, the electrodes of the array ofelectrodes connected to the first bus of the upper acoustic channelbeing aligned with the electrodes of the array of electrodes connectedto the second bus of the lower acoustic channel. 9.Surface-acoustic-wave filter according to claim 5, characterized in thatthe pitch values p₁ and p₂ are equal and in that the structure comprisestwo acoustic channels, the electrodes of each of the arrays ofelectrodes being offset by a distance p₁ between the two acousticchannels.
 10. Surface-acoustic-wave filter according to claim 1,characterized in that at least one of the arms comprises a structureequivalent to at least two parallel-connected resonators, said structurecomprising two interdigitated electrode arrays, said arrays beingconnected to a first bus and a second bus with different polarities soas to define a transducer having a central axis (Z) parallel to theelectrodes, said transducer comprising electrodes positionedsymmetrically with respect to the central axis and connected to thefirst bus and comprising electrodes positioned symmetrically withrespect to the central axis and connected to the second bus withopposite polarity, so as to excite symmetrical longitudinal modes andantisymmetrical longitudinal modes.
 11. Surface-acoustic-wave filteraccording to claim 10, characterized in that the transducer is insertedbetween two reflector arrays.
 12. Surface-acoustic-wave filter accordingto claim 1, characterized in that at least one of the arms comprises aDART type resonator with transduction cells interposed betweenreflection cells.
 13. Surface-acoustic-wave filter according to claim12, characterized in that the DART type resonator comprises resonantcavities.
 14. Surface-acoustic-wave filter according to claim 12,characterized in that the number of poles is an even number and in thatthe distance between the transduction center of a transduction cell andthe reflection center of the reflection cell adjacent to saidtransduction cell is in the range of (3±d)λ/8+kλ/2, with λ being thewavelength corresponding to the center frequency of the filter, d beingsmaller than 1 and k being an integer.
 15. Surface-acoustic-wave filtercharacterized in that it comprises the series connection of several setsof resonators, of which at least one set of resonators corresponds toclaim 1.